A courier company in downtown Dallas hand-delivers letters and small packages. T

Question

A courier company in downtown Dallas hand-delivers letters and small packages. The charge for a delivery in the city is $80. The cost for delivery outside the city but in the Metroplex area is $130. From experience the chance that a delivery is addressed in the city is 75%. This question considers revenue earned from a packet of 30 deliveries. Let X be the number of deliveries in the packet that go to Dallas. Let R be the total charge for delivering everything in the packet. (A) Find n and p such that X is equivalent to Bin(n, p). (B) Express R as a linear function of X. (C) What is the smallest possible value of R? What is the largest possible value of R? (D) Find E(X). (E) Find E(R).

Explanation / Answer

a) p = 0.75

n = 30

b) R = X * 80 + (30 - X) * 130 = 3900 - 50X

c) Smallest possible value of R is possible when X is 30, R = 3900 - 50 * 30 = 2400

Largest possible value of R is possible when X is 0, R = 3900 - 50 * 0 = 3900

d) E(X) = n * p = 30 * 0.75 = 22.5

e) E(R) = E(3900 - 50X) = 3900 - 50 * E(X) = 3900 - 50 * 22.5 = 2775

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